Infinity can be divided into infinite other infinities, amirite?

Yeah pretty much. Infinity doesn't play very nicely with our concept of arithmatic operations

by Glum-Lead 2 months ago

That's because infinity isn't a number

by Anonymous 2 months ago

True, but there are infinite numbers such as א0

by Glum-Lead 2 months ago

But aleph null etc aren't members of the ordinary algebraic rings and fields like the integers and real numbers whose properties we have become so accustomed to and take for granted. Once you introduce algebraic structures with infinities defined, the algebraic rules become different and look less like "numbers" and more like some other thing entirely. For example, all the different ways you can rotate and flip a symmetric piece of paper also form an algebraic structure called the Dihedral Group, but its properties of multiplication operate very different than the ones we're used to in the integers. Same with matrix multiplication (example of a non-abelian ring).

by kundeenrique 2 months ago

Exactly what I meant by infinity not playing nicely with our concept of arithmatics

by Glum-Lead 2 months ago

Ah yes. Indeed!

by kundeenrique 2 months ago

N@zi logo isn't a number

by Anonymous 2 months ago

Haha the irony, I was joking anyway

by Anonymous 2 months ago

Jokes have to be funny. "Haha antidemitidm am I right?" isn't a fuxking joke. Do better.

by Anonymous 2 months ago

Antisemitism? Lmao, snowflakes.

by Anonymous 2 months ago

lmao

by Anonymous 2 months ago

When you said in school that you were infinitely better than me in something, I could add +1 to infinity and win the contest. No discussion. Unless you added +2 afterwards

by Anonymous 2 months ago

Yeah but infinity (the amount of natural numbers) is provably equal to infinity+1 (the amount of non-negative integers)

by Glum-Lead 1 month ago

Because of zero?

by Anonymous 1 month ago

Yeah, adding zero doesn't change the amount of numbers

by Glum-Lead 1 month ago

Yeah but infinity (the amount of natural numbers) is provably equal to infinity+1 (the amount of non-negative integers) I mean in respect to that

by Anonymous 1 month ago

Yeah, and you understand correctly, the difference here is zero

by Glum-Lead 1 month ago

That happens lol

by Glum-Lead 1 month ago

If you use ordinals instead of cardinals, infinity + 1 and infinity + 2 are different.

by lisette49 1 month ago

Interestingly though Infinity can't be divided finitely into finite amounts.

by Anonymous 1 month ago

The real question: Is infinity divided by infinity equal to 1, or does it equal infinity?

by Anonymous 1 month ago

Infinity divided by infinity is undetermined, because the answer can be any number as well as infinity. Infinity is not something you can divide *by*.

by alexannejones 1 month ago

You'd rather have to take a really close look at the infinity - i.e. the defining term. Then you'd divide the terms and take the limit of that going to infinity. Pretty often, you're able to cancel certain parts out or apply other tricks to determine a meaningful result. (See "limit theorem".)

by Anonymous 1 month ago

That's not technically true

by oreillykarine 1 month ago

why? how do you divide by infinity?

by Anonymous 1 month ago

Renormalization is one method of dealing with/cancelling infinities

by oreillykarine 1 month ago

Is that the same thing as dividing?

by Anonymous 1 month ago

Two infinities of the same size can be cancelled out in equations

by oreillykarine 1 month ago

so not division

by Anonymous 1 month ago

How can it be "technically" true - or false? Maths aren't technical, they are theoretical.

by alexannejones 1 month ago

I should have phrased it as "Technically this is not true" Two infinities of the same size can be cancelled out. It's a pretty common mathematical trick to get around the issue 😊

by oreillykarine 1 month ago

No, you cannot cancel infinities. The infinities you are referring to are actually limits as a function approaches an asymptote. Infinity is not a number, do not treat it like a number. Treat it like a word.

by Billrodriguez 1 month ago

You seem pretty confident in that, and yet it happens all the time 😉 Infinities of the same size can be cancelled

by oreillykarine 1 month ago

You keep saying the same thing, yet you haven't given any examples to support yourself.

by Anonymous 1 month ago

No idea. Either you think x/x=1 so infinity/infinity=1 Or you think infinity x infinity is still infinity, so infinity/infinity still equals infinity.

by Anonymous 1 month ago

I think remember a proof that stated some infinities are larger than others.

by Anonymous 1 month ago

It actually can under special circumstances.

by oreillykarine 1 month ago

How? If you have a finite number of finite amounts you have a finite total, no?

by Milo23 1 month ago

Yes, because infinity is a concept and not an actual number.

by Anonymous 1 month ago

Well if you want to get really into the math infinity is a type of number. But there are a bunch of specific infinite numbers that are all different from each other and are numbers

by Milo23 1 month ago

Isnt a number also a concept?

by Dedrickaufderha 1 month ago

I would like to suggest Vsauces counting infinities video

by bboyle 1 month ago

Infinity is a necessary mathematical tool, but the common mortals like you and me can perfectly live without using it even once. When applied to physics, it creates no paradoxes, though, it merely can point at limitations of our physical theories. According to our established theories, density becomes infinite in black holes, but that doesnt mean that the density in black holes IS actually infinite. It's just the result we get from our formulas when applying them to the extremes. And this most likely means that those formulas become WRONG past a certain point.

by alexannejones 1 month ago

But how can the answer we get from our formulas when applied to extremes be ‘infinity'. It's not a number. How can ‘infinity' be the output of an equation?

by glovercody 1 month ago

It approaches infinity as a limit

by Anonymous 1 month ago

Easy : dividing by zero gives infinity as an answer. Basic maths.

by alexannejones 1 month ago

Yep I forgot to specify that, when applying to physics, we'd just use positive values since physically speaking nothing is negative. My bad. A positive number divided by zero = infinity. Black holes according to theory : a positive mass divided by a zero volume = infinite density.

by alexannejones 1 month ago

Agreed but for the context that we have here, which is maths applied to physics, we can consider we are limiting ourselves to positive values. In theoretical physics, a given mass in a volume equal to zero (black hole singularity) gives an infinite density, not an undefined one.

by alexannejones 1 month ago

Maths aren't meant to be intuitive but they are what they are. One just has to be careful when applying them to reality.

by alexannejones 1 month ago

Fair enough

by glovercody 1 month ago

Everything in math is made up but also not made up. Math kinda transcends the laws of physics. Mathematicians usually aren't thinking in terms of laws of physics at all, they're thinking in terms of math, and they see math as its own separate piece of the universe.

by Milo23 1 month ago

It's a useful concept, I don't understand your problem

by Anonymous 1 month ago

Take any two numbers There are more real numbers between them than every single possible rational number

by Anonymous 1 month ago

Uncountable vs countable infinities.

by Ashamed_Quality_361 1 month ago

Exactly!

by Anonymous 1 month ago

Infinity is a concept, not a number. Mathematic principles fall apart when a concept is placed into a numeric construct.

by Anonymous 1 month ago

Numbers are also concept

by Anonymous 1 month ago

It can also be divided into infinite finites, or finite infinities

by Anonymous 1 month ago

Oh yeah and infinity squared

by New_Shallot 1 month ago

This is why infinity is a fake and stupid idea. "Arbitrarily large number" as a concept is okay. (And that's exactly what's used in all situations where people claim infinity is useful). But an actual "infinity"? Come on bro

by Anonymous 1 month ago

There are an infinite number of different infinities each with mathematically rigorous definitions. And it's not even the weirdest thing in math

by Milo23 1 month ago

And they keep generating those definitions with desperate hope that at least one of them will be useful one day. That's the thing with math compared to, say, physics. You can just come up with stuff for no reason and with no application, but it's "rigorous", so let's publish

by Anonymous 1 month ago

Lol we don't hope that it'll be useful. We don't care at all. We do it for fun. It just happens that a lot of it ends up being useful… which is really lucky because it means we can get paid for it But also infinity math is super useful in lots of contexts

by Milo23 1 month ago

Buy also infinity math is super useful in a lots of context Yeah, and its main utility is to show that you reached the limits of a theory and achieved nonsensical results. Nonsensical entity appropriately used to signify nonsense. Example: singularity inside black holes, because at that point general relativity loses meaning and quantum effects kick in But if someone tried to compare singularities between black holes, people would appropriately consider that person a weirdo

by Anonymous 1 month ago

The singularities of black holes do not have infinities, they just have values that approach infinity, and it's the same infinity. Mathematical results involving infinities are not particularly useful for black holes. But for example cryptography and algorithmic complexity theory rely heavily on results in number theory that rely on transfinite numbers

by Milo23 1 month ago

"Arbitrarily large number" as a concept is okay. (And that's exactly what's used in all situations where people claim infinity is useful) There are a lot of scenarios where an arbitrary large number isn't helpful. If want to calculate the sum of 1/n2 for all values of n from 1 to infinity, you can do that, it's pi squared over 6. But if you want to calculate the closed form sum for 1 to 1080, you're going to struggle a lot more.

by heatherbeahan 1 month ago

And then all of those infinite infinities are all equal to each other.

by Anonymous 1 month ago